The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.

Question

A mapping diagram with one circle labeled x values containing values negative 3, negative 1, 1, 3, and 5 and another circle labeled y values containing values 0, 2, and 5 and arrows from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5.

Is the relation a function? Explain.
No, because for each input there is not exactly one output
No, because for each output there is not exactly one input
Yes, because for each input there is exactly one output
Yes, because for each output there is exactly one input

Answer 1

To determine whether the relation represented by the mapping diagram is a function, we need to check the definition of a function: a relationship in which each input (x value) has exactly one output (y value).

In this diagram:

• The x values are: -3, -1, 1, 3, 5
• The y values are: 0, 2, 5
• The arrows (which represent the mappings) are as follows:
  • -3 maps to 0
  • -1 maps to 2
  • 1 maps to 0
  • 3 maps to 2
  • 5 maps to 5

Now let's analyze the mappings:

• Both -3 and 1 map to 0 (which means that the input -3 does not have exactly one output, but shares an output with the input 1).
• Both -1 and 3 map to 2 (meaning the input -1 does not have exactly one output, but shares an output with the input 3).

Since there are inputs (specifically -3 and 1, and -1 and 3) that share the same output, the requirement for a function is violated.

Thus, the correct answer is:

No, because for each input there is not exactly one output.